nikol


Total Posts: 729 
Joined: Jun 2005 


I am looking for 'econometric' models which deliver closedform solution for predicted p.d.f..
For example, ARMA(1,1) with normal innovations delivers prediction following Normal pdf. Distribution expressed as finite decomposition of 'famous' distributions such as Normal, tStudent, Binomial, Gamma, X2 etc. is also acceptable.
Should admit that although I used quite a number of "econometric" models I still miss high level view on this subject, because never liked this 'polynomial' approach.
If you know the list from top of your head, please, share.
So far, I found this "Probabilistic time series forecasting with boosted additive models" , but that's quite not what I want... 



ronin


Total Posts: 457 
Joined: May 2006 


The general approach to that sort of thing is to write the FokkerPlanck equation for your dynamics, and then solve it for the diffusion of the delta function. BTW that's also how we know what the normal distribution looks like.
Generally, you won't be able to write a simple formula for the pdf. PDEs don't work like that. But you can still solve them numerically or asymptotically.

"There is a SIX am?"  Arthur 

nikol


Total Posts: 729 
Joined: Jun 2005 


I would love to avoid numericals as much as I can, since I would like to deliver next prediction within 50100 microseconds. If unavoidable, have to experiment with what you are saying. 



doomanx


Total Posts: 23 
Joined: Jul 2018 


Sounds like you want something Bayesian. Maybe GP regression would be a good fit, although note Bayesian is again usually solved numerically. You can use numerical methods at this timeframe if you are serious about it (this involves a lot of precomputation and efficient population of the cache). 


ronin


Total Posts: 457 
Joined: May 2006 


> next prediction within 50100 microseconds
Then do the numerics in advance and look them up at decision time. Or do some asymptotics.

"There is a SIX am?"  Arthur 


nikol


Total Posts: 729 
Joined: Jun 2005 


Lookup is good. I try to explore recurrent relationships like those in statedynamics: r_t+1 = (1w).r_t + w.e_t
It helps to save memory by keeping fewer variables.



jr


Total Posts: 3 
Joined: Apr 2017 


I would have a look at Bayesian filtering as doomanx suggests. Depending on the desired distribution I would choose some type of Kalman filter or designed my own dynamics with particle filters also known as sequential monte carlo. 


